Because the main process of interaction in the Boltzmann model of real gases is the binary collision of molecules, it is convenient to use the two-particle kinetic equation to describe the dynamics of a rarefied gas. This equation was written using the same physical assumptions as those used by Ludwig Boltzmann. The right-hand side of this equation contains the product of the linear scattering operator and chaos projector. The Boltzmann equation follows from this equation without any additional approximations after simple integration of the velocities and positions of the second particle. Using the divergence form of the scattering operator, this equation can be represented as the Liouville equation, which implies that real molecules can be replaced by quasiparticles whose distribution function is the same as that of real molecules but whose dynamics are completely different. Pairs of quasiparticles do not collide but move along continuous trajectories in the phase space. The relative velocities in pairs of quasiparticles slowly rotate with an angular velocity vector depending on the distribution function. We provide an explicit approximate expression for the angular velocity through the first few velocity moments, using a special covariant Grad expansion for the velocity distribution function, which reduces to the exact Bobylev–Kruk–Wu solution in the isotropic case. We simulated the relaxation of distribution function to equilibrium and compared results with the existing exact solutions. The described algorithm will be effective for modeling flow regions with low Knudsen numbers, where the standard Direct Monte Carlo Simulation (DSMC) method encounters significant difficulties.
Skip Nav Destination
Article navigation
September 2022
Research Article|
September 20 2022
Model two-particle kinetic equation for pairs of quasiparticles
V. L. Saveliev
V. L. Saveliev
a)
(Conceptualization, Writing – original draft, Writing – review & editing)
Fesenkov Astrophysical Institute
, Almaty, Kazakhstan
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
a)Author to whom correspondence should be addressed: [email protected]
Physics of Fluids 34, 097118 (2022)
Article history
Received:
June 27 2022
Accepted:
August 18 2022
Citation
V. L. Saveliev; Model two-particle kinetic equation for pairs of quasiparticles. Physics of Fluids 1 September 2022; 34 (9): 097118. https://doi.org/10.1063/5.0106154
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
On Oreology, the fracture and flow of “milk's favorite cookie®”
Crystal E. Owens, Max R. Fan (范瑞), et al.
Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations
Hamidreza Eivazi, Mojtaba Tahani, et al.
Chinese Academy of Science Journal Ranking System (2015–2023)
Cruz Y. Li (李雨桐), 李雨桐, et al.
Related Content
Rarefied gas simulations using quasiparticle pairs
AIP Conference Proceedings (November 2016)
Quasiparticle pairs in kinetic theory
AIP Conference Proceedings (November 2016)
Two-particle kinetic equation and its self-similar exact solutions
AIP Conf. Proc. (August 2019)
Kinetic Force Method with Quasiparticle Pairs for Numerical Modeling 3D Rarefied Gas Flows
AIP Conference Proceedings (May 2011)
Kinetic Equation for Two‐Particle Distribution Function in Boltzmann Gas Mixtures and Equation of Motion for Quasiparticle Pairs
AIP Conference Proceedings (May 2011)